# ---
# title: 1307. Verbal Arithmetic Puzzle
# id: problem1307
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: Math, Backtracking
# link: <https://leetcode.com/problems/verbal-arithmetic-puzzle/description/>
# hidden: true
# ---
# 
# Given an equation, represented by `words` on left side and the `result` on
# right side.
# 
# You need to check if the equation is solvable under the following rules:
# 
#   * Each character is decoded as one digit (0 - 9).
#   * Every pair of different characters they must map to different digits.
#   * Each `words[i]` and `result` are decoded as one number **without** leading zeros.
#   * Sum of numbers on left side (`words`) will equal to the number on right side (`result`). 
# 
# Return `True` if the equation is solvable otherwise return `False`.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: words = ["SEND","MORE"], result = "MONEY"
#     Output: true
#     Explanation: Map 'S'-> 9, 'E'->5, 'N'->6, 'D'->7, 'M'->1, 'O'->0, 'R'->8, 'Y'->'2'
#     Such that: "SEND" + "MORE" = "MONEY" ,  9567 + 1085 = 10652
# 
# **Example 2:**
# 
#     
#     
#     Input: words = ["SIX","SEVEN","SEVEN"], result = "TWENTY"
#     Output: true
#     Explanation: Map 'S'-> 6, 'I'->5, 'X'->0, 'E'->8, 'V'->7, 'N'->2, 'T'->1, 'W'->'3', 'Y'->4
#     Such that: "SIX" + "SEVEN" + "SEVEN" = "TWENTY" ,  650 + 68782 + 68782 = 138214
# 
# **Example 3:**
# 
#     
#     
#     Input: words = ["THIS","IS","TOO"], result = "FUNNY"
#     Output: true
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: words = ["LEET","CODE"], result = "POINT"
#     Output: false
#     
# 
# 
# 
# **Constraints:**
# 
#   * `2 <= words.length <= 5`
#   * `1 <= words[i].length, result.length <= 7`
#   * `words[i], result` contains only upper case English letters.
#   * Number of different characters used on the expression is at most 10.
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
